Compaq presario sr1610nx desktop.  When I turn it on, the processor fan spins and so does the psu fan.  However after a second the fans stop spinning and the computer shuts down.  At this point, the green power light on the front of the computer, that is supposed to be on when the computer is on, and off when the computer is shut down, starts blinking.

I changed about the power supply unit thinking it was the psu that had gone bad.  So what else can be making the computer shut down?  Could it be that the processor needs a new layer of thermal paste on top of it?  Im skeptical of that being the cause cause EVEN after the computer has been off for like a day or two, the same shut down prooblem happens and I cant imagine the processor getting so hot right AWAY. 

What else could it be?
1. Make sure that your CPU is dust-free(Heatsink area, processor, PSU/PSU fan, exhaust fan.
2. Reinsert your CMOS(3 Volts) Battery. Although they are the least to cause and unable to boot and shutsdown computer, It is still a part of the BOOTING process for computers.  Replacing it with a new battery is also an option.
3. Make sure all slots(PSU to the motherboard)are properly connected. Just curious...what happened prior to this ? ?Im going to blow the dust out from the heatsink , maybe it is clogged.  I dont know what else to try. 

patio:  prior to the computer acting this way, nothing was done.  The computer just gave out, maybe it was because the psu stopped working, and I say this cause the psu fan never turns on.  That is a sign that the psu is not working correct?  Is there any way a blown psu or a defective psu can damage a motherboard
It may also be a thermal issue. As you mention, check your heatsink and processor. Heatsink/s aside from getting dusty shoud also be the same smooth surface as they were first used. Check if its not a dull heatsink for it will not contribute in absorbing heat. You also mention that you already change your PSU(either the same voltage or higher). And also mention that it still shutsdown, however you noticed that there is still a blinking(green or orange) during shutdown or standby mode. I think that the PSU is good coz there is power during shutdown(Blinking). Are there any BEEPS during or when turning on first your computer? Have you change or reinsert the CMOS battery?Clear your BIOS, my shorting two jumpers usually saying "bios 1" or "Clear BIOS". Don't do this if you aren't sure. You're better off removing that battery. Put a flathead in, turn, and pop it out. Wait an hour. Put it back in. Should work. If not, let it stand for a day or two without the battery.